While I am a dog lover myself, and totally agree you cannot judge a dog by its breed, liability wise this was a no go for me.  

last month of the lease rent 2. 1/12 of the monthly rent each month.If you pay them the first months rent - what is their real inventive to just put the first person they can in there?  

Also, if they have a restricted breed, and that would cause a hardship (if you'd lose your insurance because one of your tenants had a pit bull, for instance) then you can deny that animal. 

And my pet policy specifically states name, age and breed of the one pet I allow and requires current pet records, insurance liability, etc., and forbids any other pet, including "guest" pets or pet sitting of any kind.  

If he cannot afford it under the current terms, someone else can. In

As of a few months ago.In plain English, that means if no one is looking to pull equity out or net any cash proceeds, you can in theory rate/term refinance someone else's mortgage to be in your name and (optional) have them quitclaim at the closing table.Oh, look at that, we just purchased "obtained" a house with refinance-sized closing costs instead of purchase-sized, 0% down, and a sexy 30 year fixed fannie mae interest rate. 

For pets, you'll have to know which breeds are unacceptable by your insurance carrier for coverage, set a limit on weight and require they show proof of current vaccination and registration.

@Amanda Culleton check with your insurance on which breeds they cover and never accept a prohibited breed.

Also,  I am hopeful that you have already outlined upfront what pet types/breeds you can or cannot allow, etc.  

But, you don't have that working for you, unfortunately, as it sounds like allowing pets is common.Do other rentals allow large breeds?